# from the theory of proveit.numbers.number_sets.integers¶

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
# import Expression classes needed to build the expression
from proveit import Conditional, a, b, c, d
from proveit.logic import And, Disjoint, InSet
from proveit.numbers import Integer, Interval, Less, LessEq
In [2]:
# build up the expression from sub-expressions
expr = Conditional(Disjoint(Interval(a, b), Interval(c, d)), And(InSet(a, Integer), InSet(b, Integer), InSet(c, Integer), InSet(d, Integer), And(LessEq(a, b), Less(b, c), LessEq(c, d)).with_total_ordering_style()))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\textrm{disjoint}\left(\{a~\ldotp \ldotp~b\}, \{c~\ldotp \ldotp~d\}\right) \textrm{ if } a \in \mathbb{Z} ,  b \in \mathbb{Z} ,  c \in \mathbb{Z} ,  d \in \mathbb{Z} ,  a \leq b < c \leq d\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 3
operands: 4
2Operationoperator: 19
operands: 5
3Literal
4ExprTuple6, 7
5ExprTuple8, 9, 10, 11, 12
6Operationoperator: 13
operands: 25
7Operationoperator: 13
operands: 29
8Operationoperator: 17
operands: 14
9Operationoperator: 17
operands: 15
10Operationoperator: 17
operands: 16
11Operationoperator: 17
operands: 18
12Operationoperator: 19
operands: 20
13Literal
14ExprTuple30, 21
15ExprTuple31, 21
16ExprTuple32, 21
17Literal
18ExprTuple33, 21
19Literal
20ExprTuple22, 23, 24
21Literal
22Operationoperator: 28
operands: 25
23Operationoperator: 26
operands: 27
24Operationoperator: 28
operands: 29
25ExprTuple30, 31
26Literal
27ExprTuple31, 32
28Literal
29ExprTuple32, 33
30Variable
31Variable
32Variable
33Variable